Official Quant thread for CAT 2013

@nick_baba said:
yar jo OA diya hai..its 5/6...but ho skta hai its not right...u post ur approaches..
koi explanation diya hai?
@adwaitjw said:
Let f(7)=k..... Some no...f(k)= 2k-7f(f(f(f(f(k)))))= 32k- 16*7 -8*7- 4*7- 2*7- 7So, 0=32k- 31*7k= (31/32)*7
o bhai ae ki hai..???..itna tough na ho ye...
@nick_baba said:
yar jo OA diya hai..its 5/6...but ho skta hai its not right...u post ur approaches..
Getting 35/6
@nick_baba said:
o bhai ae ki hai..???..itna tough na ho ye...
Bhai aur koi sahi tarika batado... Hume to yahi lag raha hai... Simple wala aasan tarika hoga koi to hume bhi batao...
@grkkrg said:
koi explanation diya hai?
@deedeedudu said:
Getting 35/6
koi explanation nai hai....but i think OA is right...
@nick_baba said:
koi explanation nai hai....but i think OA is right...
Yaar Goku 😃 solution post kar do
@nick_baba said:
o bhai ae ki hai..???..itna tough na ho ye...
EDIT: Yes...!! It's 35/6!!

f(f(x)) = 2f(x)-x
f(f(f(x)))= 2(2(f(x))-x)-f(x) = 3f(x) - 2x
f(f(f(f(x)))) = 4f(x) - 3x
Hence we can see the pattern now...
f(f(f(f(f(f(x)))))) = 6f(x) - 5x
=> f(7) = 5*7/6 = 35/6
@ScareCrow28 said:
Yes...!! It's 5/6!!f(f(x)) = 2f(x)-xf(f(f(x)))= 2(2(f(x))-x)-2x = 3f(x) - 2xf(f(f(f(x)))) = 4f(x) - 3Hence we can see the pattern now...f(f(f(f(f(f(x)))))) = 6f(x) - 5=> f(7) = 5/6
Bhai wont it be
f(f(f(f(f(f(x)))))) = 6f(x) - 5x?
In that case it'll come 35/6 only
@ScareCrow28 said:
Yes...!! It's 5/6!!f(f(x)) = 2f(x)-xf(f(f(x)))= 2(2(f(x))-x)-2x = 3f(x) - 2xf(f(f(f(x)))) = 4f(x) - 3Hence we can see the pattern now...f(f(f(f(f(f(x)))))) = 6f(x) - 5=> f(7) = 5/6
x kaha gaya?
f(f(f(f(f(f(x)))))) = 6f(x) - 5x
0 = 6f(7) - 5*7
f(7) = 35/6 :D
@krum
@krum said:
P(n,m)=nPm, permutationfor bijective, n=m , and no. of bijective functions = n!
Thanks so much sir
@deedeedudu said:
Bhai wont it bef(f(f(f(f(f(x)))))) = 6f(x) - 5x?In that case it'll come 35/6 only
Oh God!!! Ye kya hora hai...
You are right bhai.. It shouold be 6(f)x - 5x

@deedeedudu said:
Yaar Goku solution post kar do
yar @ScareCrow28 ne ek post kara hai... thoda confusing hai wo...
secondly , wo hexagon wale ques me liya to maine bhi edges pe 120 hai lekin usse ek baat batao....jo parallel distance hai ..wo har side pe half (i.e.1/2) nai ho jayega??...please clear it..

@ScareCrow28 said:
Yes...!! It's 5/6!!...f(f(x)) = 2f(x)-xf(f(f(x)))= 2(2(f(x))-x)-f(x) = 3f(x) - 2xf(f(f(f(x)))) = 4f(x) - 3Hence we can see the pattern now...f(f(f(f(f(f(x)))))) = 6f(x) - 5=> f(7) = 5/6
f(f(f(x)))= 2(2(f(x))-x)-"f(x)" = 3f(x) - 2x..yahan f(x) kaise le liya hai..???
@deedeedudu agar ye tareeka hai to batao plz ye f(x) kaise hai...nowhere a relation between f(x) and x is mentioned..
@deedeedudu Original post edited Question ne dimag ki dahi kardi
@nick_baba said:
yar @ScareCrow28 ne ek post kara hai... thoda confusing hai wo...secondly , wo hexagon wale ques me liya to maine bhi edges pe 120 hai lekin usse ek baat batao....jo parallel distance hai ..wo har side pe half (i.e.1/2) nai ho jayega??...please clear it..
Nahi dekh simple hai hexagon ke har vertex se perpendicular draw karo 2 wahan tk coin ka centre straight travel karega till its just above the vertex (perpendicularly)
Uske baad curved path me tb tk jab tk its just above other side (agn perpendicular)
So straight distance in essence equals to the length of side
Now angle k liye
360-(90+90+60)=120

@nick_baba said:
o bhai ae ki hai..???..itna tough na ho ye...

Calculation me galti... additional term le liya...
Kishore owns a factory of plastic goods. His production cost comprises only the cost of raw material and labour . The cost of raw material increases by 20% and the labour cost also increases from 20% to 25% of the cost of raw material. By how much percent should he reduce his consumption of raw material and labour so that his production cost remains unchanged?
1)20%
2)15%
3)17%
4)25%
5)None of these
DOUBT 2:

Do integer solutions exist for type ax+by=c and ax-by=c ?

1. When will they have a unique solution ?
2. When will they have no solution or how to determine if a solution exist?
3. How to determine 1 solution ?
4. How to determine a positive solution?
5. How to determine a general solution ?


I know the answer only for the 2nd point. Could some one help with the others ?

HOW TO DETERMINE IF A SOLUTION EXIST ?
If HCF(a,b) divides "c" or
when ax+by=1 where HCF(a,b)=1
when ax-by=1 where HCF(a,b)=1
Then there most certainly exists a solution for x and y.

NO SOLUTION:
If HCF(a,b) doesn't divide "c" or when [ax(+ or -) by=1] and HCF(a,b) is not 1

I'm not sure of the rest 😞
@nick_baba said:
f(f(f(x)))= 2(2(f(x))-x)-"f(x)" = 3f(x) - 2x..yahan f(x) kaise le liya hai..???@deedeedudu agar ye tareeka hai to batao plz ye f(x) kaise hai...nowhere a relation between f(x) and x is mentioned..
@ScareCrow28 ne thik kiya he generalized it.
Calculate kar k dekho 35/6 hi a rha.
PS: I think he has edited it and has come to @grkkrg and my side 😃 with final ans 35/6
@Shray14 said:
Kishore owns a factory of plastic goods. His production cost comprises only the cost of raw material and labour . The cost of raw material increases by 20% and the labour cost also increases from 20% to 25% of the cost of raw material. By how much percent should he reduce his consumption of raw material and labour so that his production cost remains unchanged?1)20%2)15%3)17%4)25%5)None of these
1) 20% ?